I've had decent luck with FUD, but his particular model is giving me fits.
Surface looks great in places, and in places it's quite bumpy/fuzzy.
Does this have to do with the orientation of the piece during printing?
Is this predictable in any way? There are some thin walls and small
details, so I'm not sure if I have any options.

The head on our left looks good on the upper left, and is a bit fuzzy on
the right. The right-hand and middle heads are so bad the faces are
almost completely obscured

The fuzzyness occurs where wax support material was in contact with the FUD material.

It looks like the part in the photo was printed from the bottom up. Anything at the top of the print that has no FUD directly underneath it has to have wax support material printed directly under it anyplace there's no FUD all the way to the bottom of the part. Imagine a light is directly above your part; any FUD surface that falls under shadow from the light will be fuzzy (it's where the wax support material has to be printed). See the fuzzy 'shadow' directly under all the heads on the sprue?

Your best solution is probably to print the helmets as separate pieces that are slid down onto the heads and glued. That way the facial features won't be overshadowed by the brim of the helmet and covered with support wax.

Another try, and another kind of fuzzy, in fact the surface is more ike WSF in places. Have had some fine results in the meantime, but this is unacceptable! The FUD has a coat of primer here to help show the problem I scrubbed it with a toothbrush and dishwashing liquid as vigorously as I dared, but it is part of the print, not support material. Or if it is support material, it has become one with the print.

Do those bumps appear only on the figure's right side (inside of left leg, outside of right leg)? If that's the case the print nozzle started printing your figure on its left side and the bumps are 'stringers' of material pulled off the print nozzle after it has shut off (like the thin string of toothpaste you get when you stop squeezing the tube and pull it away from the brush). They're usually extremely short and very hard to see but they probably get worse the longer the machine operates after its been serviced. They're much more numerous and longer on Frosted Detail prints: